Growing up in the 90's, I've played my share of those very entertaining, side scrolling fighting games.
Mortal Kombat, Virtual Fighters, King of Fighters, Street Fighter, Dead or Alive, and more.

Which one was your favorite?
Its very hard to choose, I guess I would go:
1.Street Fighter - first fighting game I ever played, I played this game with my cousins almost every day when I was a kid.
Favorite charater: Ken

2.Mortal Kombat - hard choice between MK and KoF but I choose MK because of its awesome fatalities.
Favorite character: Sub-Zero

3.King of Fighters - One of the most popular games in Asia, I see this game every electronic store I go to in China. If you havent played this, I recommend it.
Favorite character: Kyo or Terry

I also had Samarui Showdown, Fatal Fury, and King of Fighters on Neo Geo Home System. Way ahead of their time for home gaming.

Samurai Shodown II was the bomb with the excellent scaling graphics on the Neo Geo. Along with KOF II.

Some of my opinions.

1. Street Fighter >>>>>>>>> MK
2. SNK was the first to come up with "super" moves (Art of Fighting / Fatal Fury)
3. SNK games always had a great soundtrack
4. King of Fighters introduced multiple characters (you played with 3 characters, how awesome was that?)
5. The original 4Fiercepunch combo of Guile (jumping fierce punch, hold back+fierce punch, Fierce punch sonic boom, backhand) owns any combo back in the day. Plus it would eat 60% of your life
6. Killer Instinct introduced combos 25 hits and up.
7. SFA anime'd the fighting genre
8. Darkstalkers pushed it to its limit
9. Xmen children of the atom put it over the top
10. Tekken put fighting games back in its place